Problem: The drama club sold bags of candy and cookies to raise money for the spring show. Bags of candy cost $$7.50$, and bags of cookies cost $$2.00$, and sales equaled $$42.00$ in total. There were $2$ more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by the drama club.
Explanation: Let $x$ equal the number of bags of candy and $y$ equal the number of bags of cookies. The system of equations is then: ${7.5x+2y = 42}$ ${y = x+2}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${x+2}$ for $y$ in the first equation. ${7.5x + 2}{(x+2)}{= 42}$ Simplify and solve for $x$ $ 7.5x+2x + 4 = 42 $ $ 9.5x+4 = 42 $ $ 9.5x = 38 $ $ x = \dfrac{38}{9.5} $ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $ {y = x+2}$ to find $y$ ${y = }{(4)}{ + 2}$ ${y = 6}$ You can also plug ${x = 4}$ into $ {7.5x+2y = 42}$ and get the same answer for $y$ ${7.5}{(4)}{ + 2y = 42}$ ${y = 6}$ $4$ bags of candy and $6$ bags of cookies were sold.